Periodic self maps and thick ideals in the stable motivic homotopy category over $\mathbb{C}$ at odd primes

TL;DR

This paper investigates the structure of thick ideals generated by periodic self maps within the stable motivic homotopy category over the complex numbers at odd primes, extending known relations with classical homotopy theory.

Contribution

It introduces new insights into thick ideals in the motivic setting and extends results relating motivic Morava K-theories to classical thick ideals via Betti realization.

Findings

Characterization of thick ideals via periodic self maps

Extension of Ruth Joachimi's results to the motivic context

Relations between motivic and classical thick ideals through Betti realization

Abstract

In this article we study thick ideals defined by periodic self maps in the stable motivic homotopy category over $\mathbb{C}$. In addition, we extend some results of Ruth Joachimi about the relation between thick ideals defined by motivic Morava K-theories and the preimages of the thick ideals in the stable homotopy category under Betti realization.